Writing Equations
Write an equation to represent the following:
"A number increased by 7 is 15."
x + 7 = 15
Solve for x:
x + 6 = 14
x = 8
x + 3 > 7
x > 4
Evaluate the following:
|-6|
6
Solve for x:
x + y = 10
x = 10 - y
Twice a number decreased by 5 equals 21.
2x - 5 = 21
Solve for x:
x = -21
-2x le 10
x ge -5
Solve:
|3x - 2| = 10
x = 4, x = -8/3
Solve for y:
3x + y = 12
y = 12 - 3x
or
y= -3x + 12
A movie theater charges $8 for a ticket plus a one-time $3 fee. The total cost is $27. Write an equation to represent the situation.
8x + 3 = 27
You buy some notebooks for $4 each and spend $28 total. How many notebooks did you buy? Write and solve an equation.
4x = 28
x = 7
You owe $18 on a lunch account. You earn $3 per day helping in the cafeteria. You want your balance to be at least $0, but you can save up more. Write and solve an inequality to determine how many days you must work to get to at least $0.
x ge 6
The temperature is 4 degrees away from 10 degrees celcius. Write and solve an absolute value equation to find both possible temperatures.
|x-10| = 4
x = 14 or x = 6
The formula for total cost C = 5h + 20, where h is the number of hours worked. Solve for h.
h = (C -20)/5
A phone plan charges a $20 base fee plus $5 per gigabyte of data used. The total bill is $65.
Write and solve an equation to determine how many gigabytes were used.
20 + 5x = 65
x = 9
A gym charges a $15 sign-up fee and $12 per month. You paid $99 total.
Write and solve an equation to represent the situation. Determine how many months you paid for.
15 + 12x = 99
x = 7
A student's score is modeled by -4x + 32, where x is the number of missed questions. To pass, the student must score at least 20 points. Write and solve an inequality to determine the maximum number of questions the student can miss.
The student can miss at most 3 questions.
x le 3
A delivery location must be within 6 miles of a warehouse located at mile marker 20 on a highway.
Write and solve an absolute value equation to find the possible emile markers.
|x - 20| = 6
x = 26 or x = 14
The formula for converting Celsius to Fahrenheit is shown below. Solve for C.
F= 9/5 C + 32
C = 5/9 (F - 32)